Lesson 3.5. Rules + + = + = + 92 Lesson 3.5 ~ Multiplying Rational Numbers. Find the value of 4_. Example 1

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1 Multiplying Rational Numbers Lesson 3.5 When multiplying positive and negative rational numbers, you can determine the sign of your product before multiplying. Use the integer product rules to determine the sign of the answer. Integer PRODUCT Rules + + = + = + + = + = Example 1 Find the value of 4_ 9 ( 3 10 ). Write in simplest form. The numbers have different signs, so the answer will be negative. Multiply. Simplify. 3 4_ 9 ( 10 ) = 2 or 2 4_ 9 ( 3 10 ) = 4_ = = Lesson 3.5 ~ Multiplying Rational Numbers

2 Example 2 Find the value of 3 5 ( 2 2_ 3 ). Write in simplest form. The numbers have the same signs, so the answer will be positive. Write each mixed number as an improper fraction. Write the negative signs in the 3 5 = 16 5 and 2 2_ 3 = 8 3 numerators. Multiply. Simplify. 3 5 ( 2 2_ 3 ) = ( 3 ) = = = Example 3 The water level of Renee s swimming pool was dropping 3.4 centimeters every hour. What number represents the change in the water s depth after 0.25 hours? Write an expression to represent the situation. The numbers have different signs, so the answer will be negative. Ignore the signs while multiplying. Make the final answer negative. 3.4(0.25) Multiply the two numbers Count the number of places after the decimal point in the two factors. Move the decimal this many places in the product. Start at the right and move left. Write with the sign determined above The pool s change in depth in 0.25 hours was 0.85 centimeters. Lesson 3.5 ~ Multiplying Rational Numbers 93

3 Exercises 1. Give one reason why it might be important to determine the sign of the product before multiplying. Explain your reasoning. Find each product. Write in simplest form ( 4 ) 3. 4_ _ 4 ( 3 ) _ 4 ( 1 2_ 3 ) 6. 4 ( 2 8 ) 7. 2 ( 5 2 ) 8. Roy ran the ball on each of the last 3 plays of Friday night s football game. On each play he lost 5 4 yards. b. Write a multiplication expression to determine the number that represents the total change in yardage over the last 3 plays. c. Find the value of your expression from part b. 9. Write two fraction problems where the fractions multiply to be a positive number. One of your problems must include at least one negative number. Show all work necessary to justify your answer. 10. Vanessa s family vacationed at Jackson Hole at the end of the ski season. The family stayed at the lodge for 2 2 days. During that time, the snow level decreased 3_ 8 foot each day. b. What number represents the total change in snow depth over the past 2 2 days? Use mathematics to justify your answer. Find each product ( 0.6) ( 2) ( 0.1) (1.2) (2.5) 16. 9( 3.3) 17. During a drought, the water level in a pond decreased 2.6 centimeters each week. This continued for 4.5 weeks. b. Write a multiplication expression to determine the number that represents the total change in water depth over the past 4.5 weeks. c. Find the value of your expression from part b. 18. Alan used a meal card in the university cafeteria to pay for his lunch. Each day he used his card for lunch, the balance remaining on the card decreased by $3.62. What number represents the total change in value on his card if he used the card for 8 lunches last month? 94 Lesson 3.5 ~ Multiplying Rational Numbers

4 19. Michiko grew 3.1 cm each of the last two years and 4.5 cm each of the two years previous to that. What was her change in height over the past four years? Show all work necessary to justify your answer. 20. Bryan lost weight by walking every day. He lost an average of 1.6 kilograms each week for 7 weeks. What number represents his total change in weight? 21. Tim needs to multiply three numbers: 4.2, 5 and 2. Kyle told him that he should multiply 5 and 2 first and then multiply that by 4.2. Tim is pretty sure he needs to multiply numbers in the order they are listed. Whose strategy do you like better? Explain your reasoning. 22. Kaylin bought 2 3_ 4 pounds of carrots for $0.84 per pound. She also bought 1 2 pounds of bananas for $0.70 per pound. She handed the cashier $5.00. How much change did she receive? Show all work necessary to justify your answer. Review Find each sum or difference. Write each answer in simplest form. 23. _ _ ( 4.1) Ahn wanted to purchase six items at the grocery store. He needed to spend less than $30. The items and their prices are listed in the table at right. Do you think Ahn can buy all of the items? Explain your reasoning. ITEMS Salad $3.29 Chips $2.39 Juice $3.79 Steak $9.19 Cake $7.05 Flour $5.35 Tic-Tac-Toe ~ Cl assifications of Numbe rs There are many different classifications of numbers. Research each different classification below. Make a poster that will help other students understand the relationship between the different types of numbers. Include examples or definitions when necessary. Types of numbers: Integers Natural Numbers Rational Numbers Irrational Numbers Whole Numbers Real Numbers Lesson 3.5 ~ Multiplying Rational Numbers 95

5 Tic-Tac-Toe ~ Sci e n tific Notation Scientific notation is a method used by scientists and mathematicians to express very large and very small numbers. Scientific notation is an exponential expression using a power of 10. N 10 P Use the following process to convert a large or small number into scientific notation: Step 1: Locate the decimal point and move it left or right so there is only one non-zero digit to its left. This number represents the value of N. Step 2: Count the number of places that you moved the decimal point in Step 1. This number represents the value of P. If you moved the decimal point to the left, the sign of P is positive. If you moved the decimal point to the right, the sign of P is negative. For example: A. Convert 52,000 to scientific notation. Step 1: Move the decimal point to the left so there is only one non-zero digit to its left. 52, Step 2: Count how many places the decimal point was moved in the number above The decimal point was moved 4 places to the left. Since the decimal point was moved left, the P value is positive. Scientific notation for 52,000 is ⁴. B. Convert to scientific notation. Step 1: Move the decimal point to the right so there is only one non-zero digit to its left Step 2: Count how many places the decimal point was moved in the number above The decimal point was moved 3 places to the right. Since the decimal point was moved right, the P value is negative. Scientific notation for is Write each large or small number in scientific notation , ,000,000, ,400, , ,000,000,000, Find a very large number that represents something in nature. Explain what the number represents and write this number in standard notation and scientific notation. 14. Find a very small number that represents something in nature. Explain what the number represents and write this number in standard notation and scientific notation. 96 Lesson 3.5 ~ Multiplying Rational Numbers